View source for Biography:Roberto Longo (mathematician)

{{short description|Italian mathematician}}
{{Infobox scientist
| name = Roberto Longo
| image = Roberto Longo Lago di Sabaudia 2019.jpg
| birth_place = [[Place:Rome|Rome]], Italy
| nationality = Italian
| field = [[Mathematics]]
| work_institution = {{Unbulleted list|[[Organization:University of Pennsylvania|University of Pennsylvania]]|[[Organization:University of California, Berkeley|University of California, Berkeley]]|[[Organization:University of Rome Tor Vergata|University of Rome Tor Vergata]]}}
| alma_mater = [[Organization:Sapienza University of Rome|Sapienza University of Rome]]
| academic_advisors = [[Biography:Sergio Doplicher|Sergio Doplicher]]
| thesis_title = Tomita-Takesaki modular structure for AFD von Neumann algebras
| thesis_year = 1975
| awards = {{Unbulleted list |Humboldt Prize {{smaller|(2016){{nbsp|2}}}}|Medaglia dei XL {{smaller|(2021){{nbsp|2}}}}}}
}}

'''Roberto Longo''' (born 9 May 1953) is an Italian mathematician, specializing in [[Operator algebra|operator algebra]]s and [[Physics:Quantum field theory|quantum field theory]].<ref>{{cite web|title=Roberto Longo|website=Department of Mathematics, University of Rome Tor Vergata|url=http://www.mat.uniroma2.it/longo/|access-date=February 19, 2021}}</ref>

== Education and career ==
Roberto Longo graduated in Mathematics<ref>The academic degree is ''[[Social:Laurea|Laurea]] in Matematica'' and was the highest academic title at the epoch.</ref> at the [[Organization:Sapienza University of Rome|Sapienza University of Rome]] in 1975 under the supervision of the mathematical physicist [[Biography:Sergio Doplicher|Sergio Doplicher]].<ref>The thesis is {{cite thesis|last=Longo|first=Roberto|date=1975|title=Tomita-Takesaki modular structure for AFD von Neumann algebras|place=Rome}} {{MathGenealogy|id=100244}}</ref> From 1975 to 1977 Longo was a [[Social:Predoctoral fellow|predoctoral fellow]] of the Consiglio Nazionale delle Ricerche and later [[Social:Assistant professor|assistant professor]] at the Sapienza University of Rome, where he became an [[Social:Associate professor|associate professor]] in 1980. In 1987 he was nominated full professor of [[Functional analysis|functional analysis]] at the [[Organization:University of Rome Tor Vergata|University of Rome Tor Vergata]] and since 2010 he is the director of the [[Organization:Center for Mathematics and Theoretical Physics|Center for Mathematics and Theoretical Physics]] in Rome.

Between 1978 and 1979 he was [[Visiting scholar|visiting scholar]] at the [[Organization:University of Pennsylvania|University of Pennsylvania]] and the [[Organization:University of California, Berkeley|University of California, Berkeley]]. He has been a visiting professor in numerous research centers, including the CNRS in Marseille, the [[Organization:Mathematical Sciences Research Institute|Mathematical Sciences Research Institute]] in Berkeley, California, the [[Organization:Harvard University|Harvard University]], MIT, and the University of Göttingen.<ref name=CV>{{cite web|title=Roberto Longo, Curriculum Vitae|website=University of Rome Tor Vergara|url=http://www.mat.uniroma2.it/longo/Home_files/CV-2010.pdf|access-date=February 19, 2021}}</ref>

Longo is an expert in the theory of operator algebras and its applications to quantum field theory. His work influenced the structural analysis of quantum field theory, especially of [[Conformal field theory|conformal field theory]], and opened up to new developments in model building methods of interest in local quantum physics.<ref name=Humboldt>{{cite web|url=https://www.humboldt-foundation.de/en/connect/explore-the-humboldt-network/singleview?tx_rsmavhsolr_solrview%5BpPersonId%5D=1154986&cHash=13869c9b9202d59fc4928bef1b780146|title=Humboldt Foundation member page of Roberto Longo|website=humboldt-foundation.de|access-date=February 19, 2021}}</ref>

Roberto Longo is known in particular for his work with Sergio Doplicher on split inclusions of [[Von Neumann algebra|von Neumann algebra]]s<ref>{{cite journal|last1=Doplicher|first1=S.|last2=Longo|first2=R.|title=Standard and split inclusions of von Neumann algebras|journal=Inventiones Mathematicae|volume=75|issue=3|year=1984|pages=493–536|issn=0020-9910|doi=10.1007/BF01388641|url=https://eudml.org/doc/143108|bibcode=1984InMat..75..493D|s2cid=121819323}}</ref> and for having solved, independently with [[Biography:Sorin Popa|Sorin Popa]], the Stone-Weierstrass conjecture for factorial states.<ref>{{cite journal|last=Longo|first=Roberto|title=Solution of the factorial Stone-Weierstrass conjecture. An application of the theory of standard split W*-inclusions|journal=Inventiones Mathematicae|volume=76|number=1|year=1984|pages=145–155|doi=10.1007/BF01388497|bibcode=1984InMat..76..145L|s2cid=122775835}}</ref> He also found the relationship between the statistical dimension<ref>{{Cite journal|last1=Doplicher|first1=Sergio|last2=Haag|first2=Rudolf|last3=Roberts|first3=John E.|title=Local observables and particle statistics. 1|journal=Communications in Mathematical Physics|volume=23|pages=199–230|year=1971|issue=3|doi=10.1007/BF01877742|bibcode=1971CMaPh..23..199D|s2cid=189833852|url=http://projecteuclid.org/euclid.cmp/1103857630 }}</ref> and the Jones index.<ref>{{cite journal|arxiv=funct-an/9604008|last1=Longo|first1=Roberto|last2=Roberts|first2=John E.|title=A Theory of Dimension|journal=K-Theory|year=1997|volume=11|issue=2|pages=103–159|doi=10.1023/A:1007714415067|bibcode = 1996funct.an..4008L|s2cid=119581477}}</ref> In a work with Yasuyuki Kawahigashi, Longo classified the discrete series of conformal chiral networks of von Neumann algebras.<ref>{{cite journal|title=Classification of local conformal nets: Case c < 1|journal=Annals of Mathematics|volume=160|pages=493–522|year=2004|last1=Kawahigashi|first1=Yasuyuki|last2=Longo|first2=Roberto|issue=2|doi=10.4007/annals.2004.160.493|arxiv=math-ph/0201015|s2cid=7145642}}</ref> Together with Vincenzo Morinelli and Karl-Henning Rehren, he also showed that particles with infinite spin cannot appear in a local theory.<ref>{{cite journal|last1=Longo|first1=Roberto|last2=Morinelli|first2=Vincenzo|last3=Rehren|first3=Karl-Henning|title=Where Infinite Spin Particles Are Localizable|journal=Communications in Mathematical Physics|volume=345|year=2016|issue=2|pages=587–614|doi=10.1007/s00220-015-2475-9|arxiv=1505.01759|bibcode=2016CMaPh.345..587L|s2cid=119569712}}</ref> His most recent works concern [[Physics:Entropy|entropy]] and [[Information theory|information]] for infinite [[Physics:Quantum system|quantum system]]s.<ref>{{cite journal|last1=Ciolli|first1=Fabio|last2=Longo|first2=Roberto|last3=Ruzzi|first3=Giuseppe|title=The information in a wave|journal=Communications in Mathematical Physics|volume=379|year=2019|issue=3|pages=979–1000|doi=10.1007/s00220-019-03593-3|arxiv=1906.01707|bibcode=2019CMaPh.379..979C|s2cid=174799030}}</ref>

== Honors and awards ==
In 1994 Longo was an invited speaker at the International Congress of Mathematicians in Zurich.<ref>{{cite web|title=ICM Plenary and Invited Speakers|website=mathunion.org|url=https://www.mathunion.org/icm-plenary-and-invited-speakers?combine=longo|access-date=February 19, 2021}} {{cite book|author=Longo, Roberto|chapter=Von Neumann algebras and quantum field theory|title=Proceedings of the International Congress of Mathematicians, 1994, Zürich|volume=2|pages=1281–1291|year=1995}}</ref> He was invited speaker at the [[Physics:International Congress on Mathematical Physics|International Congress on Mathematical Physics]] in 1981 in [[Place:Berlin|Berlin]],<ref>{{cite book|author=Longo, Roberto|chapter=Modular Automorphisms of Local Algebras in Quantum Field Theory|title=6th International Conference on Mathematical Physics - Congress of Association for Mathematical Physics|pages=372–373|year=1981|place=Berlin}}</ref> in 1988 in Swansea,<ref>{{cite book|author=Longo, Roberto|chapter=Inclusions of Von Neumann Algebrass and Quantum Field Theory|title=IX International Conference on Mathematical Physics (IAMP)|pages=472–474|year=1988|place=Swansea}}</ref> in 1994 in [[Place:Paris|Paris]],<ref>{{cite book|author=Longo, Roberto|chapter=Inclusions of von Neumann algebras and superselection structures|title=11th International Conference on Mathematical Physics (ICMP-11)|place=Paris|pages=342–351|year=1994}}</ref> and in 2003 in [[Place:Lisbon|Lisbon]].<ref>{{cite web|title=ICMP 2003 schedule|website=XIV ICMP Lisbon|url=http://icmp2003.net/schedule/|access-date=February 19, 2021}}</ref> In 2004 he was Andrejewski Lecturer in Göttingen.<ref>{{cite web|title=Mathematisches Institut - Andrejewski Vorlesung|website=uni-math.gwdg.de|url=https://www.uni-math.gwdg.de/andrej/longo.html|access-date=February 23, 2021|language=de}}</ref> He was a plenary speaker at the International Congress of Mathematicians in 2009 in [[Place:Prague|Prague]]<ref>{{cite web|title=Plenary Speakers|website=ICMP Prague|url=http://icmp.ujf.cas.cz/confirmed-plenary-speakers.htm|access-date=February 19, 2021}}</ref> and at ''Strings 2018'' in Okinawa.<ref>{{cite web|title=''Modular theory and Bekenstein's bound'' by Robert Longo, partly based on a joint work with Feng Xu|website=Okinawa, OIST, Strings 2018|url=https://indico.oist.jp/indico/event/5/picture/116.pdf|access-date=February 19, 2021}}</ref>

In 2013 he was elected a Fellow of the American Mathematical Society<ref>{{cite web|url=https://www.ams.org/cgi-bin/fellows/fellows.cgi#d|title=List of Fellows of the American Mathematical Society|website=American Mathematical Society|access-date=February 19, 2021}} {{cite journal|last=Jackson|first=Allyn|title=Fellows of the AMS: Inaugural Class|journal=Notices of the AMS|volume=60|number=5|year=2013|pages=631–637|url=https://www.ams.org/profession/ams-fellows/rnoti-p631.pdf}}</ref> and in 2021 a member of the [[Organization:Academia Europaea|Academia Europaea]].<ref>{{cite web|url=https://www.ae-info.org/ae/Member/Longo_Roberto|title=Longo's member page of Academia Europæa|website=Academia Europæa|access-date=July 20, 2021}}</ref> He was awarded in 2016 the Humboldt Research Award<ref name=Humboldt/><ref>{{Cite journal|title=Humboldt-Preisträger|journal=Uni Inform, Göttingen|date=April 2015|page=5|language=de}}</ref> 
and in 2021 the XL medal from the Accademia Nazionale delle Scienze detta dei XL for his in-depth and innovative research in operator algebras and in conformal field theory.<ref>{{cite web|url=https://web.uniroma2.it/module/name/Content/newlang/italiano/navpath/HOM/action/showpage/content_id/94622|title=A Roberto Longo la Medaglia dei XL per la Matematica 2021|website=uniroma2.it|language=it|access-date=July 20, 2021}}</ref> In 2013 the conference ''Mathematics and Quantum Physics'' at the Lincei National Academy was dedicated to him on the occasion of his 60th birthday.<ref>{{cite web|url=http://cmtp.uniroma2.it/13MQP/|title=Mathematics and Quantum Physics Conference|website=cmtp.uniroma2.it|access-date=February 19, 2021}}</ref> In 2008<ref>{{Cite journal|title = Scienze, Roma trionfa negli Advanced grants|journal = Il Sole 24 Ore, Roma|number = 40|date = October 15, 2008|language=it}} {{cite web|title=Advanced Grants: Operator Algebras and Conformal Field Theory|website=europa.eu|url=https://cordis.europa.eu/project/id/227458|access-date=February 25, 2021}}</ref> and in 2015<ref>{{cite web|title=Advanced Grants: Quantum Algebraic Structures and Models|website=europa.eu|url=https://cordis.europa.eu/project/id/669240|access-date=February 25, 2021}}</ref> he received two Advanced Grants from the European Research Council.<ref>{{cite web|title=Un matematico di Tor Vergata vincitore dell'"Advanced Grants"|website=maddmaths.simai.eu|url=http://maddmaths.simai.eu/news-2/roberto-longo-si-aggiudica-il-suo-secondo-erc-con-un-progetto-su-matematica-e-fisica-quantistica/|access-date=February 23, 2021|language=it}}</ref> In 2018 he was member of the sectional panel ''Mathematical Physics'' of the International Congress of Mathematicians in Rio de Janeiro.<ref>{{cite web|url=https://www.mathunion.org/fileadmin/IMU/ICM2018/Panelists_2018.pdf|title=Sectional Panels for ICM 2018|website=mathunion.org/icm/past-icms|access-date=February 19, 2021}}</ref>

== Selected publications ==
{{div col|colwidth=35em}}
* {{cite journal|doi=10.1007/BF01208372|title=Modular structure of the local algebras associated with the free massless scalar field theory|journal=Communications in Mathematical Physics|volume=84|issue=1|pages=71–85|year=1982|last1=Hislop|first1=Peter D.|last2=Longo|first2=Roberto|bibcode=1982CMaPh..84...71H|s2cid=119856852|url=http://projecteuclid.org/euclid.cmp/1103921046 }}
* {{cite journal|last1=Doplicher|first1=S.|last2=Longo|first2=R.|title=Standard and split inclusions of von Neumann algebras|journal=Inventiones Mathematicae|volume=75|issue=3|year=1984|pages=493–536|issn=0020-9910|doi=10.1007/BF01388641|url=https://eudml.org/doc/143108|bibcode=1984InMat..75..493D|s2cid=121819323}}
* {{cite journal|last=Longo|first=Roberto|title=Solution of the factorial Stone-Weierstrass conjecture. An application of the theory of standard split W*-inclusions|journal=Inventiones Mathematicae|volume=76|number=1|year=1984|pages=145–155|doi=10.1007/BF01388497|bibcode=1984InMat..76..145L|s2cid=122775835}}
* {{cite journal|doi=10.1007/BF02125124|title=Index of subfactors and statistics of quantum fields. I|journal=Communications in Mathematical Physics|volume=126|issue=2|pages=217–247|year=1989|last1=Longo|first1=Roberto|bibcode=1989CMaPh.126..217L|s2cid=122420613|url=http://projecteuclid.org/euclid.cmp/1104179850 }}
* {{cite journal|last=Longo|first=Roberto|title=A duality for Hopf algebras and for subfactors. I|journal=Communications in Mathematical Physics|volume=159|issue=1|year=1994|pages=133–150|issn=0010-3616|doi=10.1007/BF02100488|url=https://projecteuclid.org/euclid.cmp/1104254494|bibcode=1994CMaPh.159..133L|s2cid=123347247}}
* {{cite journal|doi=10.1007/BF02101672|title=The conformal spin and statistics theorem|journal=Communications in Mathematical Physics|volume=181|issue=1|pages=11–35|year=1996|last1=Guido|first1=Daniele|last2=Longo|first2=Roberto|bibcode=1996CMaPh.181...11G|arxiv=hep-th/9505059|s2cid=17663903}}
* {{cite journal|arxiv=funct-an/9604008|last1=Longo|first1=Roberto|last2=Roberts|first2=John E.|title=A Theory of Dimension|journal=K-Theory|year=1997|volume=11|issue=2|pages=103–159|doi=10.1023/A:1007714415067|bibcode = 1996funct.an..4008L|s2cid=119581477}}
* {{cite journal|doi=10.1007/PL00005565|title=Multi-Interval Subfactors and Modularity of Representations in Conformal Field Theory|journal=Communications in Mathematical Physics|volume=219|issue=3|pages=631–669|year=2001|last1=Kawahigashi|first1=Yasuyuki|last2=Longo|first2=Roberto|last3=Müger|first3=Michael|bibcode=2001CMaPh.219..631K|arxiv=math/9903104|s2cid=15568392}}
* {{cite journal|title=Classification of local conformal nets: Case c < 1|journal=Annals of Mathematics|volume=160|pages=493–522|year=2004|last1=Kawahigashi|first1=Yasuyuki|last2=Longo|first2=Roberto|issue=2|doi=10.4007/annals.2004.160.493|arxiv=math-ph/0201015|s2cid=7145642}}
* {{cite journal|last1=Kac|first1=Victor G.|last2=Longo|first2=Roberto|last3=Xu|first3=Feng|title=Solitons in affine and permutation orbifolds|journal=Communications in Mathematical Physics|volume=253|year=2004|issue=3|pages=723–764|doi=10.1007/s00220-004-1160-1|arxiv=math/0312512|s2cid=14298134}}
* {{cite journal|last1=Longo|first1=Roberto|last2=Witten|first2=Edward|title=An Algebraic Construction of Boundary Quantum Field Theory|journal=Communications in Mathematical Physics|volume=303|year=2011|issue=1|pages=213–232|doi=10.1007/s00220-010-1133-5|arxiv=1004.0616|bibcode=2011CMaPh.303..213L|s2cid=115174261}}
* {{cite journal|last1=Longo|first1=Roberto|last2=Morinelli|first2=Vincenzo|last3=Rehren|first3=Karl-Henning|title=Where Infinite Spin Particles Are Localizable|journal=Communications in Mathematical Physics|volume=345|year=2016|issue=2|pages=587–614|doi=10.1007/s00220-015-2475-9|arxiv=1505.01759|bibcode=2016CMaPh.345..587L|s2cid=119569712}}
* {{cite journal|last1=Carpi|first1=Sebastiano|last2=Kawahigashi|first2=Yasuyuki|last3=Longo|first3=Roberto|last4=Weiner|first4=Mihály|title=From vertex operator algebras to conformal nets and back|journal=Memoirs of the American Mathematical Society|volume=254|number=1213|year=2018|doi=10.1090/memo/1213|arxiv=1503.01260|s2cid=119618626}}
* {{cite journal|last1=Ciolli|first1=Fabio|last2=Longo|first2=Roberto|last3=Ruzzi|first3=Giuseppe|title=The information in a wave|journal=Communications in Mathematical Physics|volume=379|year=2019|issue=3|pages=979–1000|doi=10.1007/s00220-019-03593-3|arxiv=1906.01707|bibcode=2019CMaPh.379..979C|s2cid=174799030}}
{{div col end}}

== See also ==
* [[Physics:Axiomatic quantum field theory|Axiomatic quantum field theory]]
* Local quantum physics
* [[Operator algebra]]
* [[Physics:Quantum field theory|Quantum field theory]]

== References ==
<references/>

== External links ==
* {{MathGenealogy|id=100244|title=Roberto Longo}}.
* {{zbMATH|id=longo.roberto}}.
* {{cite web|title=Center for Mathematics and Theoretical Physics webpage|website=Center for Mathematics and Theoretical Physics|url=http://cmtp.uniroma2.it/|access-date=February 21, 2021}}
* {{cite web|title=Longo's personal webpage|website=uniroma2.it|url=https://www.mat.uniroma2.it/longo/|access-date=February 21, 2021}}
* {{cite web|title=Longo's seminar in the conference about the 50 years of algebraic quantum field theory|website=gwdg.de|url=https://www.uni-math.gwdg.de/aufzeichnungen/AQFT50/Longo/|date=July 30, 2009|access-date=February 19, 2021}}
* {{cite web|first=Roberto|last=Longo|title=KMS states in Conformal Field Theory|date=July 6, 2016|publisher=Hausdorff Center for Mathematics|website=YouTube|url=https://www.youtube.com/watch?v=DuzdXw_Yldg|access-date=February 19, 2021}}
* {{cite web|first=Roberto|last=Longo|title=Noncommutative Geometry: State of the Art and Future Prospects, Alain Connes 70th Birthday|date=2017|place=Shanghai|website=mat.uniroma2.it|url=https://www.mat.uniroma2.it/longo/Videos_files/Shanga17-video.mp4|access-date=February 21, 2021}}
* {{cite web|first=Roberto|last=Longo|title=Discussion about the Landauer principle (and bound)|date=June 12, 2017|website=Isaac Newton Institute for Mathematical Sciences|url=https://www.newton.ac.uk/seminar/20170612143015301|access-date=February 21, 2021}}
* {{cite web|first=Roberto|last=Longo|title=The Information in a Wave|date=May 5, 2020|website=YouTube|url=https://www.youtube.com/watch?v=n7svXoev7H0|access-date=February 21, 2021}}


{{DEFAULTSORT:Longo, Roberto}}
[[Category:Mathematical physicists]]

{{Sourceattribution|Roberto Longo (mathematician)}}